When I touch an object that I'm meant to pass through I spin randomly out of control
First, make sure that "Ghost" is checked and "obstacle" and "collision bounds" are unchecked in physics. Check that the base and top face are far enough up apart on the Z axis so they do not collide with the avatar. You may want to change the cube into a plane to prevent this from becoming a problem.
It would help to know what version of blender, it may be a bug, and what your logic bricks look like.